Convex Functions, Partial Orderings, and Statistical Applications PDF Download

Author: Josip E. Peajcariaac
Publisher: Academic Press
ISBN: 0080925227
Category : Mathematics
Languages : en
Pages : 485

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Book Description
This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists. Presents classical and newly published results on convex functions and related inequalities Explains partial ordering based on arrangement and their applications in mathematics, probability, statsitics, and reliability Demonstrates the connection of partial ordering with other well-known orderings such as majorization and Schur functions Will generate further research and applications

Author: J. E. Pečarić
Publisher:
ISBN:
Category :
Languages : en
Pages : 469

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Book Description

Author: Constantin P. Niculescu
Publisher: Springer
ISBN: 3319783378
Category : Mathematics
Languages : en
Pages : 430

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Book Description
Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Author: Boris Mordukhovich
Publisher: Springer Nature
ISBN: 3031024060
Category : Mathematics
Languages : en
Pages : 202

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Book Description
Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.

Author: Jonathan M. Borwein
Publisher: Cambridge University Press
ISBN: 1139811096
Category : Mathematics
Languages : en
Pages : 533

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Book Description
Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Author: Themistocles M. Rassias
Publisher: Springer Nature
ISBN: 3030725634
Category : Mathematics
Languages : en
Pages : 791

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Book Description
This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers–Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg–Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Author: Huan-nan Shi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110607867
Category : Mathematics
Languages : en
Pages : 256

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Book Description
This two-volume work introduces the theory and applications of Schur-convex functions. The second volume mainly focuses on the application of Schur-convex functions in sequences inequalities, integral inequalities, mean value inequalities for two variables, mean value inequalities for multi-variables, and in geometric inequalities.

Author: Johann Pfanzagl
Publisher: Springer
ISBN: 3642310842
Category : Mathematics
Languages : en
Pages : 321

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Book Description
This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Author: Wai Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Book Description
Hardy, Littlewood and Polya (1934) introduced the notion of one function being convex with respect to a second function and developed some inequalities concerning the means of the functions. We use this notion to establish a partial order called convex-ordering among functions. In particular, the distribution functions encountered in many parametric families in reliability theory are convex-ordered. We have formulated some inequalities which can be used for testing whether a sample comes from F or G, when F and G are within the same convex family. Performance characteristics of different coherent structures can also be compared with respect to this partial ordering. For example, we will show that the reliability of a k+l-out-of-n system is convex with respect to the reliability of a k-out-of-n system. When F is convex with respect to G, the tail of the distribution F is heavier than that of G; therefore, our convex ordering implies stochastic ordering. The ordering is also related to total positivity and monotone likelihood ratio families. This provides us a tool to obtain some useful results in reliability and mathematical statistics.

Author: Shigeru Furuichi
Publisher: MDPI
ISBN: 3039280627
Category : Mathematics
Languages : en
Pages : 204

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Book Description
Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.